Excursions in Brownian motion
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This article is published in Arkiv för Matematik.The article was published on 1976-12-01 and is currently open access. It has received 222 citations till now. The article focuses on the topics: Brownian motion.read more
Citations
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Journal ArticleDOI
Thermodynamics for the zero-level set of the Brownian bridge
TL;DR: The random set of instants where the Brownian bridge vanishes is constructed in terms of a random branching process as mentioned in this paper, and the Hausdorff measure supported by this set is shown to be equivalent to the partition function of a special class of disordered systems.
Dissertation
Parisian excursions of Brownian motion and their applications in mathematical finance
TL;DR: In this paper, a semi-closed form solution for the density of the one-sided stopping times of Parisian excursions is proposed, which does not require any numerical iterations of Laplace transforms.
Journal ArticleDOI
Excursions and Lévy System of Boundary Process
Ping He,Jiangang Ying +1 more
TL;DR: In this article, the joint distribution of end points of excursion away from a closed set straddling on a fixed time was investigated and the result was used to compute the Levy system and the Dirichlet form of the boundary process.
Posted Content
Asymptotic behavior and moderate deviation principle for the maximum of a Dyck path
TL;DR: In this article, the authors obtained a large and moderate deviation principle for the law of the maximum of a random Dyck path, and extended the results of Chung, Kennedy, Kaigh and Khorunzhiy and Marckert.
Journal ArticleDOI
Asymptotic behavior and the moderate deviation principle for the maximum of a Dyck path
TL;DR: In this article, the authors obtained a large and moderate deviation principle for the law of the maximum of a random Dyck path, extending the results of Chung, Kennedy, and Khorunzhiy and Marckert.
References
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Book
Diffusion Processes and their Sample Paths
Kiyosi Itô,Henry P. McKean +1 more
TL;DR: In this article, the authors consider the problem of approximating the Brownian motion by a random walk with respect to the de Moivre-laplace limit theorem and show that it is NP-hard.
Journal Article
Sur certains processus stochastiques homogènes
TL;DR: In this paper, the authors implique l'accord avec les conditions générales d'utilisation (http://www.compositio.org/legal.php).
BookDOI
Aufgaben und Lehrsätze aus der Analysis: Erster Band: Reihen · Integralrechnung Funktionentheorie
Book
Brownian motion and diffusion
TL;DR: The book as discussed by the authors is part of a trilogy covering the field of Markov processes and provides a readable and constructive treatment of Brownian motion and diffusion, which dispenses with most of the customary transform apparatus.
Journal ArticleDOI
Functional Central Limit Theorems for Random Walks Conditioned to Stay Positive
TL;DR: In this article, it was shown that the conditional and unconditional weak limit for a sequence of independent, identically distributed random variables is the same as that of the standard Brownian motion.